Periodic solutions for quaternion-valued fuzzy cellular neural networks with time-varying delays

$2p$ -th Moment Global Exponential Stability of a Unique $2P$ -th Mean Almost Periodic Oscillation for Semi-Discrete Takagi-Sugeno Fuzzy Stochastic Cellular Neural Networks With Time Delays

“…These applications mainly depend on the property of stablity of CNNs. Therefore, the stability of CNNs received widespread attentions in the last decades, see [2]- [4], [20]- [22], [54]. In [54], Mo et al studied the stability of CNNs with linear, sigmoid and tangent sigmoid functions.…”

Existence and global exponential stability of anti-periodic solutions for quaternion-valued cellular neural networks with time-varying delays

“…Fortunately, over the past 20 years, especially in algebra area, quaternion has been a topic for the effective applications in the real world. Also, a new class of differential equations named quaternion differential equations has been already applied successfully to the fields, such as quantum mechanics [2,3], robotic manipulation [4], fluid mechanics [5], differential geometry [6], communication problems and signal processing [7][8][9], and neural networks [10][11][12][13]. Many scholars tried to shed some light on the information about solutions of quaternion differential equations.…”

“…Curves of x R p (t) = (x R 1 (t), x R 2 (t)) T and x I p (t) = (x I 1 (t), x I 2 (t)) T of system(12) with the initial values (x R 1 (0), x R 2 (0)) T = (0.5, -0.1) T , (-0.25, 0.35) T , (0.15, -0.45) T and (x I 1 (0), x I 2 (0)) T = (0.4, -0.2) T , (0.2, -0.45) T , (-0.3, 0.1) T 0.01 + 0.03j cos 8t + 0.01k 0.01 + 0.02j sin 2 4t + 0.01k sin 8t, sin 4t + 1 2 i sin 4t +1 10 j cos 4t + 1 20 k sin 2 2t.By computing, T = π 4 , f 1 (x) = f 2 (x) ≤ 0.089, g 1 (x) = g 2 (x) ≤ 0.097,a + 1 08, b + 11 ≤ 0.051, b + 12 ≤ 0.0245, b + 21 ≤ 0.055, b + 22 ≤ 0.0245, c + 11 ≤ 0.023, c + 12 ≤ 0.034, c + 21 ≤ 0.034, c + 22 ≤ 0.025, Q 1 ≤ 0.5, Q 2 ≤ 0.55. So (H 1 ), (H 2 ) and (H 3 ) are satisfied.…”

Pseudo almost automorphic solutions of quaternion-valued neural networks with infinitely distributed delays via a non-decomposing method

“…Therefore, there are some research results in this area. Since the quaternion multiplication does not satisfy the commutative law, most of the results are obtained by decomposing the considered quaternion-valued systems into real-valued systems or a complex-valued systems [13][14][15][16][17][18][19]. Only very few results on the stability and dissipation of quaternion-valued neural networks are obtained by direct method [20][21][22].…”